If we are talking a neanderthal vs. a normal, non-violent office worker then the neanderthal will probably win

Put the neanderthal against a UFC fighter or some other kind of professional fighter, my money is on modern man.

We’re built bigger, more mass...it’d be like a UFC fighter fighting against a guy from three weight classes down. It’s also much more likely that we’ll be able to adjust attack / defense patterns quicker than neanderthals.